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This paper deals with the possibility of using a feedforward neural network to test the discrepancies between a real astronomical image and a predefined template. This task can be accomplished thanks to the capability of neural networks to solve a nonlinear approximation problem, i.e. to construct an hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with some conveniently chosen statistical moments, evaluated along the $\{x, y\}$ axes; in this...

Functions of the form $\sum_{i = 1}^{N} f_{i} (x) g_{i} (t)$ in $L_{2}$

František Neuman (1982)

Archivum Mathematicum

General Haar systems and greedy approximation

Anna Kamont (2001)

Studia Mathematica

We show that each general Haar system is permutatively equivalent in $L^{p} ([0, 1])$ , 1 < p < ∞, to a subsequence of the classical (i.e. dyadic) Haar system. As a consequence, each general Haar system is a greedy basis in $L^{p} ([0, 1])$ , 1 < p < ∞. In addition, we give an example of a general Haar system whose tensor products are greedy bases in each $L^{p} ({[0, 1]}^{d})$ , 1 < p < ∞, d ∈ ℕ. This is in contrast to [11], where it has been shown that the tensor products of the dyadic Haar system are not greedy bases in $L^{p} ({[0, 1]}^{d})$ for 1...

High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials

George A. Hagedorn (1987)

Annales de l'I.H.P. Physique théorique

Integral Kernels and Approximation on Totally Real Submanifolds of Cn.

Bo Berndtsson (1979)

Mathematische Annalen

Interpolation mit Intervallfunktionalen.

Manfred Reimer, Franz Pittnauer (1976)

Mathematische Zeitschrift

$L_{p}$ -approximation by iterative combination of Phillips operators.

Gupta, Vijay, Agrawal, P.N. (1992)

Publications de l'Institut Mathématique. Nouvelle Série

$L_{p}$ -inverse theorem for modified beta operators.

Gupta, Vijay, Maheshwari, Prerna, Jain, V. K. (2003)

International Journal of Mathematics and Mathematical Sciences

Lemmes de Schwarz et lemmes d'approximations p-adiques en plusieurs variables.

P. Robba (1978)

Inventiones mathematicae

Linear combinations of partitions of unity with restricted supports

Christian Richter (2002)

Studia Mathematica

Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation $f = \sum_{C \in} a_{C} φ_{C}$ with $a_{C} \in E$ and a partition of unity $φ_{C} : C \in$ subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction ${f |}_{P}$ attains its extrema at vertices of P. Finally, a class of extremal functions on the metric space...

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